Expressiveness Modulo Bisimilarity: A Coalgebraic Perspective

Venema, Yde

doi:10.1007/978-3-319-06025-5_2

Cited by 8 publications

(25 citation statements)

References 25 publications

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“…In the following we shall not take care to distinguish between such a monotone predicate lifting and the corresponding atomic formula. The proof of the following result closely follows that of the main result in [17]. The main difference with [17] is that here we need an "unravelling"-like component.…”

Section: Bisimulation Invariancementioning

confidence: 53%

“…The proof of the following result closely follows that of the main result in [17]. The main difference with [17] is that here we need an "unravelling"-like component. Proof.…”

Section: Bisimulation Invariancementioning

confidence: 53%

“…The most important concept that we take from [17] is that of a uniform translation (called uniform correspondence in [17]):…”

Section: Bisimulation Invariancementioning

confidence: 99%

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Monadic Second-Order Logic and Bisimulation Invariance for Coalgebras

Enqvist

Seifan

Venema

2015

2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science

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Generalizing standard monadic second-order logic for Kripke models, we introduce monadic second-order logic MSO T interpreted over coalgebras for an arbitrary set functor T. Similar to well-known results for monadic second-order logic over trees, we provide a translation of this logic into a class of automata, relative to the class of T-coalgebras that admit a tree-like supporting Kripke frame. We then consider invariance under behavioral equivalence of MSO T -formulas; more in particular, we investigate whether the coalgebraic µ-calculus is the bisimulation-invariant fragment of MSO T . Building on recent results by the third author we show that in order to provide such a coalgebraic generalization of the Janin-Walukiewicz Theorem, it suffices to find what we call an adequate uniform construction for the functor T. As applications of this result we obtain a partly new proof of the Janin-Walukiewicz Theorem, and bisimulation invariance results for the bag functor (graded modal logic) and all exponential polynomial functors.Finally, we consider in some detail the monotone neighborhood functor M, which provides coalgebraic semantics for monotone modal logic. It turns out that there is no adequate uniform construction for M, whence the automata-theoretic approach towards bisimulation invariance does not apply directly. This problem can be overcome if we consider global bisimulations between neighborhood models: one of our main technical results provides a characterization of the monotone modal µ-calculus extended with the global modalities, as the fragment of monadic second-order logic for the monotone neighborhood functor that is invariant for global bisimulations.

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Section: Bisimulation Invariancementioning

confidence: 53%

“…The proof of the following result closely follows that of the main result in [17]. The main difference with [17] is that here we need an "unravelling"-like component. Proof.…”

Section: Bisimulation Invariancementioning

confidence: 53%

See 1 more Smart Citation

Monadic Second-Order Logic and Bisimulation Invariance for Coalgebras

Enqvist

Seifan

Venema

2015

2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science

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“…Following a similar approach as Janin & Walukiewicz [8], our proof will then revolve around a map from Autcw(FOE ∞ 1 ) to Autcw(FO1), guided by the additional insight from [16] that such a link can already be determined by a translation on the level of the one-step languages FOE ∞ 1 and FO1.…”

Section: Automatamentioning

confidence: 97%

“…The proof is based on a fairly routine comparison of the acceptance games A(A • , T) and A(A, T ω ). In a slightly more general setting, the details can be found in [16].…”

Section: Modal Characterization Of Wmsomentioning

confidence: 98%

Weak MSO

Carreiro

Facchini

Venema

et al. 2014

Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Nin

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We prove that the bisimulation-invariant fragment of weak monadic second-order logic (WMSO) is equivalent to the fragment of the modal µ-calculus where the application of the least fixpoint operator µp.ϕ is restricted to formulas ϕ that are continuous in p.Our proof is automata-theoretic in nature; in particular, we introduce a class of automata characterizing the expressive power of WMSO over tree models of arbitrary branching degree. The transition map of these automata is defined in terms of a logic FOE ∞ 1 that is the extension of first-order logic with a generalized quantifier ∃ ∞ , where ∃ ∞ x.ϕ means that there are infinitely many objects satisfying ϕ. An important part of our work consists of a modeltheoretic analysis of FOE ∞ 1 .

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Model theory of monadic predicate logic with the infinity quantifier

et al. 2021

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This paper establishes model-theoretic properties of $$\texttt {M} \texttt {E} ^{\infty }$$ M E ∞ , a variation of monadic first-order logic that features the generalised quantifier $$\exists ^\infty $$ ∃ ∞ (‘there are infinitely many’). We will also prove analogous versions of these results in the simpler setting of monadic first-order logic with and without equality ($$\texttt {M} \texttt {E} $$ M E and $$\texttt {M} $$ M , respectively). For each logic $$\texttt {L} \in \{ \texttt {M} , \texttt {M} \texttt {E} , \texttt {M} \texttt {E} ^{\infty }\}$$ L ∈ { M , M E , M E ∞ } we will show the following. We provide syntactically defined fragments of $$\texttt {L} $$ L characterising four different semantic properties of $$\texttt {L} $$ L -sentences: (1) being monotone and (2) (Scott) continuous in a given set of monadic predicates; (3) having truth preserved under taking submodels or (4) being truth invariant under taking quotients. In each case, we produce an effectively defined map that translates an arbitrary sentence $$\varphi $$ φ to a sentence $$\varphi ^\mathsf{p}$$ φ p belonging to the corresponding syntactic fragment, with the property that $$\varphi $$ φ is equivalent to $$\varphi ^\mathsf{p}$$ φ p precisely when it has the associated semantic property. As a corollary of our developments, we obtain that the four semantic properties above are decidable for $$\texttt {L} $$ L -sentences.

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Expressiveness Modulo Bisimilarity: A Coalgebraic Perspective

Cited by 8 publications

References 25 publications

Monadic Second-Order Logic and Bisimulation Invariance for Coalgebras

Monadic Second-Order Logic and Bisimulation Invariance for Coalgebras

Weak MSO

Model theory of monadic predicate logic with the infinity quantifier

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